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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 
 

 

Wave equation in the plane driven by a general stochastic measure


Authors: I. M. Bodnarchuk and V. M. Radchenko
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 73-90
MSC (2010): Primary 60H15; Secondary 60G17, 60G57
DOI: https://doi.org/10.1090/tpms/1063
Published electronically: August 19, 2019
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Abstract: We study the Cauchy problem for the wave equation on the plane driven by a general stochastic measure. The existence and uniqueness of a mild solution is proved. The Hölder continuity with respect to both the time and spatial variables is established for the trajectories of a solution. The continuous dependence of a solution on the initial data of the problem is proved.


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Additional Information

I. M. Bodnarchuk
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: ibodnarchuk@univ.kiev.ua

V. M. Radchenko
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: vradchenko@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/1063
Keywords: Stochastic measure, stochastic wave equation, mild solution, H\"older condition, Besov space
Received by editor(s): February 22, 2018
Published electronically: August 19, 2019
Article copyright: © Copyright 2019 American Mathematical Society